Best Known (61−16, 61, s)-Nets in Base 27
(61−16, 61, 66430)-Net over F27 — Constructive and digital
Digital (45, 61, 66430)-net over F27, using
- net defined by OOA [i] based on linear OOA(2761, 66430, F27, 16, 16) (dual of [(66430, 16), 1062819, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2761, 531440, F27, 16) (dual of [531440, 531379, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2761, 531441, F27, 16) (dual of [531441, 531380, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2761, 531441, F27, 16) (dual of [531441, 531380, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2761, 531440, F27, 16) (dual of [531440, 531379, 17]-code), using
(61−16, 61, 316878)-Net over F27 — Digital
Digital (45, 61, 316878)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2761, 316878, F27, 16) (dual of [316878, 316817, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2761, 531441, F27, 16) (dual of [531441, 531380, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2761, 531441, F27, 16) (dual of [531441, 531380, 17]-code), using
(61−16, 61, large)-Net in Base 27 — Upper bound on s
There is no (45, 61, large)-net in base 27, because
- 14 times m-reduction [i] would yield (45, 47, large)-net in base 27, but